932

932 = 2 x 2 x 233.

932 has a representation as a sum to two squares: 932 = 16² + 26².

932 is the maximum number of regions into which 31 circles divide the plane.

932 is the number of permutations of length 9 within distance 2 of a fixed permutation (A002524).

932 is the sum of five distinct positive pentatope numbers (A104396).

Source: On-Line Encyclopedia of Integer Sequences

1305

1305 = 3 x 3 x 5 x 29.

1305 has two representations as a sum of two squares: 1305 = 3² + 36² = 24² + 27².

1305 is the number of graphs with 11 vertices and 9 edges.

1305 is 909 in base 12.

1305 is a number n such that n² (1703025) can be obtained by inserting internal (but not necessarily contiguous) digits (A046851).

Source: What's Special About This Number?

6115

6115 = 5 x 1223.

6115 is a number n such that n² - 6 and n² + 6 are both prime (A108403).

6115 is the number of S, E, and NW-moving king's tours on a 13 x 13 board summed over all starting positions (A187510).

6115 Martinduncan is an asteroid discovered in 1984 and named in honor of astronomer Martin J. Duncan of Queen's University, Kingston, Ontario.

Source: On-Line Encyclopedia of Integer Sequences

624

624 = 2 x 2 x 2 x 2 x 3 x 13.

624 is 4444 in base 5. It is 1551 in base 7.

624 is the smallest number with the property that its first five multiples (624, 1248, 1872, 2496, 3120) contain the digit 2.

624 is the sum of twin primes: 624 = 311 + 313.

624 Hektor is the largest of the Jupiter Trojan asteroids.

Source: What's Special About This Number?

729

729 = 3 x 3 x 3 x 3 x 3 x 3 = 3⁶. It is a perfect sixth power.

729 is a centered octagonal number.

728 and 729 are consecutive Smith numbers, so they are known as Smith brothers.

729 is the smallest odd cube represented as the sum of two prime numbers: 729 = 2 + 727.

729 is a cube that is the sum of three cubes: 729 = 9³ = 1³ + 6³ + 8³.

729 = 27² = (1 + 2 + 2 + 2 + 4 + 4 + 4 + 8)² = 1³ + 2³ + 2³ + 2³ + 4³ + 4³ + 4³ + 8³.

729 is 1331 in base 8 and 121 in base 26.

Source: Prime Curios!

618

618 = 2 x 3 x 103.

618 = 0!² + 1!² + 2!² + 3!² + 4!².

618 is 4433 in base 5.

618 is the sum of 10 positive fifth powers (A003355): 618 = 3⁵ + 3⁵ + 2⁵ + 2⁵ + 2⁵ + 2⁵ + 1⁵ + 1⁵ + 1⁵ + 1⁵.

618 is the number of ternary squarefree words of length 15 (A006156).

Source: What's Special About This Number?

566

566 = 2 x 283.

566 is the number of ways to place 24 points on a 12 x 12 grid so that no three points are on a line (A000769).

The sum of the fourth power of the prime factors of 566 is a prime (A134620): 2⁴ + 283⁴ = 6414247937, a prime.

566 is the sum of five distinct pentatope numbers (A104395).

566 is the sum of the first 20 primes minus the next prime (A166448).

Source: What's Special About This Number?

409

409 is a prime number.

409 is a centered triangular number.

409 has a representation as a sum of two squares: 409 = 3² + 20².

409 is the hypotenuse of a primitive Pythagorean triple: 409² = 120² + 391².

409 is the smallest prime that, along with both its prime neighbors, uses non-prime digits: 401, 409, 419.

409 is the number of primes less than 10,000 that form members of twin prime pairs.

Source: Prime Curios!

815

815 = 5 x 163.

815 is a Lucas 3-step number.

815 is 3435 in base 6.

815² is the sum of three consecutive primes (A076304).

815 and 817 are both semiprimes (A136196).

Source: What's Special About This Number?

121

121 = 11 x 11.

121 is the smallest multidigit palindromic square. It is also the smallest palindromic composite such that some permutation of digits is prime. It is the only odd palindromic square with an odd number of digits that is divisible by a palindromic prime number with an even number of digits.

121 is a perfect square. It is also a centered octagonal number and a centered dodecagonal number.

Every number greater than 121 is the sum of distinct primes of the form 4n + 1.

121 is 11111 in base 3.

121 is the maximum number of regions into which 15 lines divide a plane.

121 can be expressed as the sum of a prime and its reversal for exactly three distinct primes: 121 = 29 + 92 = 47 + 74 = 83 + 38.

121 = 1 + 3¹ + 3² + 3³ + 3⁴.

121 is the number of points required to win a standard game of cribbage.

Source: Prime Curios!

802

802 = 2 x 401.

802 is the number of ways to toss a coin 10 times and not get a run of five (A135492).

802 has a representation as a sum of two squares: 802 = 19² + 21².

802 is 414 in base 14.

802 is the sum of eight consecutive primes (A127335): 802 = 83 + 89 + 97 + 101 + 103 + 107 + 109 + 113.

802² is the sum of two consecutive primes (A074924): 802² = 643204 = 321593 + 321611.

802 is the number of isomers of the hydrocarbon chemical compound C₁₃H₂₈.

Source: On-Line Encyclopedia of Integer Sequences

401

401 is a prime number.

401 is the start of the first occurrence of three consecutive primes using no prime digits: 401, 409, 419.

401 is the sum of seven consecutive primes: 401 = 43 + 47 + 53 + 59 + 61 + 67 + 71. It is also the sum of nine consecutive primes: 401 = 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61.

401 is a divisor of 20⁴ - 1.

401 has a representation as a sum of two squares: 401 = 1² + 20².

401 is the hypotenuse of a primitive Pythagorean triple: 401² = 40² + 399².

401 was the hull number of the RMS Titanic.

Source: Number Gossip

783

783 = 3 x 3 x 3 x 29.

783 is a heptagonal number.

783 is the number of 11-ominoes that tile the plane by translation.

783³ = 480,048,687 = (48 + 00 + 48 + 687)³.

783 is 373 in base 15 and 234 in base 19.

Source: What Special About This Number?

679

679 = 7 x 97.

679 is the smallest number with multiplicative persistence 5 (A003001 and A064869).

679 is the sum of three consecutive primes: 679 = 223 + 227 + 229 (A034961). It is also the sum of nine consecutive primes (A127336): 679 = 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89 + 97.

679 is the sum of nine positive fifth powers (A003354): 679 = 3⁵ + 3⁵ + 2⁵ + 2⁵ + 2⁵ + 2⁵ + 2⁵ + 2⁵ + 1⁵.

The sum of the digits of 679 (6 + 7 + 9 = 22) exceeds the sum of the digits of 679² (4 + 6 + 1 + 0 + 4 + 1 = 17) (A064399).

Source: Number Gossip

494

494 = 2 x 13 x 19.

494 has the representation 494 = 2⁹ - 18.

The product of the first 494 composite numbers minus 1 is prime.

494 + 209 = 703 and 494,207 = 703².

494 is 3434 in base 5.

Source: Prime Curios!

868

868 = 2 x 2 x 7 x 31.

4⁸⁶⁸ - 3 is a prime number.

868 has a square root whose decimal part starts with the digits 1 to 9 in some order: 29.461839725. . .

868 is 4004 in base 6 (A029963).

868 is the number of ways of writing 60 as a sum of eight nonnegative cubes (A173681).

Source: Prime Curios!

396

396 = 2 x 2 x 3 x 3 x 11.

396 is a nonagonal number.

396 is the number of positions in a 3 x 3 sliding puzzle that require exactly 11 moves to solve starting with the hole in a corner.

396 is 112200 in base 3 and 1500 in base 6.

396 is the sum of a twin prime pair: 396 = 197 + 199.

396 refers to the displacement in cubic inches of early Chevrolet Big-Block engines.

Source: What's Special About This Number?

296

296 = 2 x 2 x 2 x 37.

296 is the number of integer partitions of 30 into distinct parts.

296 has a representation as a sum of two squares: 296 = 10² + 14².

296 x 333,667 = 98,765,432.

296 is 1212 in base 6.

Source: What's Special About This Number?

252

252 = 2 x 2 x 3 x 3 x 7.

252 is the smallest number that is the product of two distinct numbers that are reverse of each other: 252 = 12 x 21.

252 = 2⁸ - 4.

252 is the third value of Ramanujan's tau function (A000594).

252 is a hexagonal pyramidal number.

If you flip a coin 10 times in a row, there are exactly 252 ways in which it can turn out that you get exactly five heads and five tails.

Source: Number Gossip

574

574 = 2 x 7 x 41.

574 is the maximum number of pieces into which a torus can be cut by 14 slices.

574 is 210021 in base 3. It is 707 in base 9.

574 is the number of sevens among the digits of all four-digit primes (A152279).

574² = 329476 contains exactly six different digits (A054034).

Source: What's Special About This Number?

759

759 = 3 x 11 x 23. It is the product of three distinct Sophie Germain primes (A157346).

759 is 1001010 in base 3. It is 3303 in base 6 and 1033 in base 9 (and 2133 in base 7 and 533 in base 12).

759 is the sum of five consecutive primes (A034964): 759 = 139 + 149 + 151 + 157 + 163.

759 is a triangular matchstick number (A045943).

759 is the number of sets of natural numbers less than 37 that sum to 37 (A111133).

Source: On-Line Encyclopedia of Integer Sequences

662

662 = 2 x 331.

662 is a divisor of 31³ - 1.

662 is the index of the smallest triangular number that contains the digits 1, 2, 3, 4, and 5 (219,453).

662 is 220112 in base 3 and 22112 in base 4. It is 10122 in base 5 and 3022 in base 6.

662 is the sum of 12 consecutive primes (A127339): 662 = 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79.

Source: What's Special About This Number?

753

753 = 3 x 251.

753 is a divisor of 20¹⁰ - 1.

753 is the smallest composite number that you can get by concatenating all odd primes up to some number in decreasing order.

753 is the smallest number whose cube contains four consecutive sevens: 753³ = 426957777.

753 is 353 in base 15.

Source: Number Gossip

139

139 is a prime number.

137 and 139 form a twin prime pair.

139 is a divisor of 42³ - 1.

139 is the smallest prime that retains the end (unit) digit of its successor (149). 139 and 149 are the first consecutive primes differing by 10.

139 is the smallest prime with one prime digit, one composite digit, and one digit that is neither prime nor composite.

139 divides the sum of the first 139 composite numbers.

139 is the smallest prime number whose product of digits is a prime cube: 1 x 3 x 9 = 27 = 3³.

139 Juewa is a large, dark, main-belt asteroid discovered in 1874.

Source: Number Gossip

370

370 = 2 x 5 x 37.

370 is a decagonal number (A001107).

370/(3 + 7 + 0) = 37 is prime.

370 = 37 x (3 + 7) = 3³ + 7³. It is an Armstrong or narcissistic number (A005188) because it is equal to the sum of the cubes of its three digits.

370 is the average of the sum of all the possible permutations of its digits: (037 + 073 + 307 + 370 + 703 + 730)/6 = 370.

370 is the sum of four consecutive primes: 370 = 83 + 89 + 97 + 101.

370 has two representations as a sum of two squares: 370 = 3² + 19² = 9² + 17².

Source: Prime Curios!

946

946 = 2 x 11 x 43.

946 is the 43rd triangular number (A000217). It is the sum of all integers from 1 to 43.

946 is also a hexagonal number (A000384), a centered nonagonal number, and a hexagonal pyramidal number (A002412).

946 is the only three-digit number such that the reversal of the concatenation of the first 946 natural numbers is a prime.

946 is the largest known number n such that n is the sum of two consecutive primes but not the sum of two sums of two consecutive primes.

Source: Prime Curios!

224

224 = 2 x 2 x 2 x 2 x 2 x 7.

224 has a unique representation as a sum of three squares: 224 = 4² + 8² + 12².

224 is an abundant number (A005101).

The number 224 times 422 (its reversal) plus 1 and plus 3 are twin primes (94529 and 94531).

224 is an Entringer number (A008281).

224 is the sum of four consecutive cubes: 224 = 2³ + 3³ + 4³ + 5³.

There are 224 ounces in a stone (14 pounds).

Source: Prime Curios!

635

635 = 5 x 127.

635 is a number whose 5th root has a decimal part that begins with 635 (3.63542128. . .).

635⁴ = 162590400625, a concatenation of square numbers (16, 25, 9, 0, 400, 625).

635 is the sum of nine consecutive primes: 635 = 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89.

The sum of the digits of 635 is equal to the sum of the digits of the 635th prime (4703).

Source: What's Special About This Number?

732

732 = 2 x 2 x 3 x 61.

732 = 1⁷ + 2⁶ + 3⁵ + 4⁴ + 5³ + 6² + 7¹.

732 = 3⁶ + 3.

732 is a divisor of 13³ - 1.

732 is 444 in base 13. It is 606 in base 11.

Source: What's Special About This Number?

161

161 = 7 x 23.

161 is a divisor of 22² - 1.

161 is a hexagonal pyramidal number.

161 is a Cullen number.

Every number greater than 161 is the sum of distinct primes of the form 6n - 1.

161 is the smallest semiprime that yields a palindromic prime (191) when turned upside down.

161 is the sum of five consecutive prime numbers: 161 = 23 + 29 + 31 + 37 + 41.

There are 161 ways to bet on a roulette wheel.

Source: Prime Curios!

722

722 = 2 x 19 x 19.

722 has a representation as a sum of two squares: 722 = 19² + 19².

722 is the sum of the fourth powers of the first three primes (A133531): 722 = 2⁴ + 3⁴ + 5⁴.

722 is the sum of two distinct factorials, the sum of the factorials of the digits of 26 (A061602): 722 = 2! + 6!

722 is the maximum number of regions into which the plane can be divided by 10 (concave) quadrilaterals (A077591).

Source: What's Special About This Number?

151

151 is a prime number.

149 and 151 form a twin prime pair.

151 is a centered decagonal number.

151 is the smallest palindromic prime sandwiched between two consecutive squareful (or non-squarefree) numbers.

151 is the smallest prime that begins a 3-run of sums of five consecutive primes: 151 + 157 + 163 + 167 + 173 = 811; and 811 + 821 + 823 + 827 + 829 = 4111, and 4111 + 4127 + 4129 + 4133 + 4139 = 20639. Can you find the smallest 4-run example?

The Statue of Liberty, from its base to the tip of its torch, was designed to be 151 feet tall.

Source: Prime Curios!

231

231 = 3 x 7 x 11. It is the 22nd number that is the product of three distinct primes.

231 is 11100111 in base 2 (binary).

231 is the number of integer partitions of 16.

231 is the 21st triangular number. It is the smallest triangular number in which the sum of the external digits equals the sum of the internal digits.

231 is a hexagonal number and an octahedral number.

231 = 2² + 3² + 7² + 13².

The U.S. liquid gallon is defined as 231 cubic inches.

Source: Number Gossip

913

913 = 11 x 83.

The integer digits of 913² = 833569 are exactly the same (albeit in a different order) as the integer digits of 914² = 835396 (A072841).

The digit sum of 913 equals the digit sum of its prime factors (A036920).

913 is a generalized polygonal number (A080859).

913 is the sum of the integers from 1 to 43, excluding perfect fifth powers (A132336).

Source: On-Line Encyclopedia of Integer Sequences

318

318 = 2 x 3 x 53.

The sum of the digits of 318 is one less than the sum of the digits of its prime factors.

318 is the number of unlabeled partially ordered sets of 6 elements.

318 is the sum of 12 consecutive primes: 318 = 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47.

318 is 2233 in base 5. It is 383 in base 9.

Source: Prime Curios!

523

523 is a prime number.

521 and 523 form a twin prime pair.

523 together with 541 form the smallest two consecutive primes such that the sums of their digits are equal. It is the smallest prime that is followed immediately by 17 composite numbers.

523 is the only three-digit prime containing all three of the first three prime digits. It is the largest prime with a prime number of distinct prime digits. It is the only prime formed from three consecutive primes, one being the sum of the other two.

523 is 313 in base 13.

523 is the sum of seven consecutive primes: 523 = 61 + 67 + 71 + 73 + 79 + 83 + 89.

Source: Number Gossip

1651

1651 = 13 x 127.

1651 is 11001110011 in base 2 (binary) (A048700).

1651 is a heptagonal number (A000566).

1651 is a potential magic constant of a 7 x 7 magic squares composed of consecutive primes (A188536).

1651 is the sum of eight but not fewer squared primes (A183215).

Source: On-Line Encyclopedia of Integer Sequences

7698

7698 = 2 x 3 x 1283.

7698² = 59259204.

7698 is the number of ways to place 10 non-attacking kings on a 4 x 10 chessboard (A061593).

The set of base 7 digits of 7698 equals the set of base 9 digits of 7698 (A037439): {0, 1, 3, 5}.

7698 is a number n for which 12n + 1, 12n + 5, 12n + 7, and 12n + 11 are primes (A123985).

Source: On-Line Encyclopedia of Integer Sequences

765

765 = 3 x 3 x 5 x 17.

765 has two representations as a sum of two squares: 765 = 6² + 27² = 18² + 21².

765 = 401 + 263 + 89 + 7 + 5. Its reversal, 567, is the smallest number that is the sum of different primes using all ten digits.

765 is 1011111101 in base 2 (A006995) and 636 in base 11.

765 is the sum of eight positive fifth powers (A003353): 765 = 3⁵ + 3⁵ + 3⁵ + 2⁵ + 1⁵ + 1⁵ + 1⁵ + 1⁵.

Source: Prime Curios!

204

204 = 2 x 2 x 3 x 17.

204 is 11001100 in base 2 (binary).

204 is a nonagonal number and a square pyramidal number. It is also an abundant number.

The number 204ⁿ + 1 is prime for n = 2, 0, and 4.

204 is the square root of the triangular number 41616.

204² = 23³ + 24³ + 25³ = 41616.

204 is the sum of twin primes: 204 = 101 + 103.

204 is the number of different squares that you can find on a standard chessboard.

Source: Number Gossip

1518

1518 = 2 x 3 x 11 x 23.

1518 is a divisor of 47¹⁰ - 1.

1518 is the sum of its proper divisors that contain the digit 5: 1518 = 253 + 506 + 759.

1518 is the sum of two consecutive sums of consecutive numbers: 1518 = 121 + 122 + . . . + 131 + 132 = 133 + 134 + . . . + 142 + 143.

1518 is 2002020 in base 3. It is 330 in base 22.

Source: What's Special About This Number?

758

758 = 2 x 379.

758 is the maximum number of regions into which 28 circles divide the plane.

758 is 464 in base 13 and 262 in base 18.

758 is the number of walks on a cubic 4 x 4 x 4 lattice (starting at the origin and not going below the x-y plane) (A005573).

758 is the smallest of three consecutive integers (758, 759, 760) divisible by three consecutive primes respectively (2, 3, 5) (A073607).

Source: On-Line Encyclopedia of Integer Sequences

391

391 = 17 x 23.

391 is a Smith number (A0906753). The sum of its digits (3 + 9 + 1 = 13) equals the sum of the digits of its prime factors (1 + 7 + 2 + 3 = 13).

391 is a centered pentagonal number (A005891).

391 is 474 in base 9 (A029955).

391 is a substring of 2³⁹¹ (A032740).

391, 393, and 395 are all semiprimes (A092125), between the prime numbers 389 and 397.

Source: On-Line Encyclopedia of Integer Sequences

473

473 = 11 x 43.

473 is the largest known number whose square (223729) and fourth power (50054665441) use different digits (and no digit 8).

473 x 8 = 3784 (same digits are used on both sides).

473 is 575 in base 9.

473 is the sum of five consecutive primes (A034964): 473 = 83 + 89 + 97 + 101 + 103.

473 is the number of ways of making change for 51 cents using coins of 1, 2, 5, 10, 20, and 50 cents (A001313).

Source: What's Special About This Number?

965

965 = 5 x 193.

965 has two representations as a sum of two squares: 965 = 2² + 31² = 17² + 26²
(A088909).

965 is the hypotenuse of two primitive Pythagorean triples (A024409): 965² = 124² + 957² = 387² + 884² (A165158).

Both 965 and 965² = 931225 have the same initial digit and the same final digit (A086457).

965 is the number of unit squares at least 50% covered by a circle inscribed in an integer square of size 35 x 35 (A051233).

Source: On-Line Encyclopedia of Integer Sequences

1400

1400 = 2 x 2 x 2 x 5 x 5 x 7.

1400 is a divisor of 99² - 1.

1400 is the number of different arrangements of 4 non-attacking queens on a 4 x 10 chessboard (A061990).

1400 is 4040 in base 7.

1400 is divisible by the square of the sum of its digits (25) (A072081).

1400 is the sum of the digits in the 41st row of Pascal's triangle (A066600).

Source: What's Special About This Number?

656

656 = 2 x 2 x 2 x 2 x 41.

656 is 1010010000 in base 2 (binary). It is a palindrome in base 3 (220022) (A007633 and A014190), base 9 (808), and base 10 (656) (A029965).

656 has a representation as a sum of two squares: 656 = 16² + 20².

656 has 10 binary digits and 10 divisors (1, 2, 4, 8, 16, 41, 82, 164, 328, 656) (A135772).

656 plus the 656th prime produces a triangular number (A115882): 656 + 4909 = 5565.

Source: What's Special About This Number?

848

848 = 2 x 2 x 2 x 2 x 53.

848 has a representation as a sum of two squares: 848 = 8² + 28².

848 is the number of inequivalent binary linear codes of length 9.

848 is the sum of the first 33 nonprimes (A051349).

848 is the sum of distinct factorials (A059590): 848 = 6! + 5! + 3! + 2!

Source: What's Special About This Number?

938

938 = 2 x 7 x 67.

938 is the number of lines passing through at least two points of an 8 x 8 grid of points (A018808).

938 is the total number of positive integers below 10⁵ requiring two positive cubes in their representation as a sum of cubes (A181375).

938 is the smallest of three consecutive integers (938, 939, 940) divisible by three consecutive primes respectively (2, 3, 5) (A073607).

938 is the sum of two consecutive primes and all the composite numbers in between (A174518): 938 = 131 + 132 + 133 + 134 + 135 + 136 + 137.

Source: What's Special About This Number?

191

191 is a prime number. It is a Sophie Germain prime because 2 x 191 + 1 = 383 is also a prime. In addition, the resulting number is a palindrome.

191 and 193 form a twin prime pair.

191 is the maximum number of regions into which 19 lines divide the plane.

191 is the smallest palindromic prime whose digit sum (1 + 9 + 1 = 11) is a multidigit palindromic prime. It is also the smallest multidigit palindromic prime that yields a palindrome when multiplied by the next prime: 191 x 193 = 36863.

191 is the smallest prime in a set of four consecutive primes (191, 193, 197, 199) whose sum of digits is another set of four primes (11, 13, 17, 19).

The common U.S. coins--a silver dollar, half-dollar, quarter, dime, nickel, and penny--add up to 191 cents.

Source: Number Gossip